Question

An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,800. They are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. They randomly select 40 claims, and calculate a sample mean of $1,950. Assuming that the standard deviation of claims is $500, and set α = .05, test to see

a. Write down the type of test you will conduct.

b. Write down the null and alternative hypotheses.

c. Construct the test statistic.

d. Conduct the test

e. What do you conclude

Answer 1

a. Write down the type of test you will conduct.

Here, we have to use one sample z test for the population mean.

b. Write down the null and alternative hypotheses.

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: The average claim amount is $1,800.

Alternative hypothesis: H_a: The average claim amount is greater than $1,800.

H₀: µ = 1800 versus H_a: µ >1800

This is an upper tailed test.

c. Construct the test statistic.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 1800

Xbar = 1950

σ = 500

n = 40

α = 0.05

Critical value = 1.6449

(by using z-table or excel)

Z = (1950 - 1800)/[500/sqrt(40)]

Z = 1.8974

d. Conduct the test

P-value = 0.0289

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

e. What do you conclude?

There is not sufficient evidence to conclude that the average claim amount is greater than $1,800.